Question
‘A’ alone can complete a work in 30 days. ‘B’
alone can complete the same work in 40 days. If ‘A’ and ‘B’ work together for 6 days, then the remaining work can be completed by ‘A’ alone in how many days?Solution
Let the total amount of work = 120 units {LCM of 30 and 40} Then, efficiency of ‘A’ = 120/30 = 4 units/day Efficiency of ‘B’ = 120/40 = 3 units/day Combined efficiency of ‘A’ and ‘B’ = 4 + 3 = 7 units/day Work completed by ‘A’ and ‘B’ together in 6 days = 7 × 6 = 42 units Remaining work = 120 – 42 = 78 units Time taken by ‘A’ alone to complete the remaining work = 78/4 = 19.5 days
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